ON THE THIRD ORDER SOLUTION OF KdV EQUATION BY USING HOMOTOPY PERTURBATION METHOD

In this research, we discussed the solution of the KdV equation using the Homotopy Perturbation method. The KdV equation that describes the water wave equation is solved by using the mixing method between Homotopy and Perturbation methods. Homotopy was built with embedding parameter p E [0,1], which undergoes a deformation process from linear problems to nonlinear problems, and the assumed solution of the KdV equation is expressed in the form of a power series p up to the third order. The result shows that in each order solution, we obtained resonance term. For handling the condition, we used the Lindsteadt-Poincare method. The wave number k2 and dispersion relation w can be obtained in the second-order solution as the effect of using the Lindsteadt-Poincare method.